Abstract: We demonstrate photon-mediated interactions between two individually trapped
atoms coupled to a nanophotonic cavity. Specifically, we observe superradiant
line broadening when the atoms are resonant with the cavity, and level
repulsion when the cavity is coupled to the atoms in the dispersive regime. Our
approach makes use of individual control over the internal states of the atoms,
their position with respect to the cavity mode, as well as the light shifts to
tune atomic transitions individually, allowing us to directly observe the
anti-crossing of the superradiant and subradiant two-atom states. These
observations open the door for realizing quantum networks and studying quantum
many-body physics based on atom arrays coupled to nanophotonic devices.